Padres general manager Josh Byrnes said Cashner was injured by a hunting partner while they were trimming a carcass and that the 26-year-old right-hander sustained a small cut and had surgery on the punctured tendon.
While the injury is considered minor, the former first-round draft pick will be sidelined for three months before he can start a throwing program.
Cashner was selected by the Chicago Cubs with the 19th overall pick in the 2008 amateur draft and traded to the Padres last January. He was 3-4 with a 4.27 ERA in five starts and 28 relief appearances this year.
On Tuesday, Chicago Cubs manager Dale Sveum said he was OK after former teammate Robin Yount accidentally shot him in the right ear and back with pellets during a recent quail hunt in Arizona.